Distance against time graphs
distance
time
Constant speed
distance
The gradient of this
graph gives the speed
time
Getting faster (accelerating)
distance
time
A car accelerating from stop and
then hitting a wall
distance
time
Speed against time graphs
speed
time
No movement
speed
time
Constant speed
speed
time
Getting faster? (accelerating)
speed
Constant acceleration
time
Getting faster? (accelerating)
v
speed
The gradient of this
graph gives the
acceleration
a=v–u
t
(v= final speed, u = initial speed)
u
time
Getting faster? (accelerating)
speed
The area under the graph
gives the distance travelled
time
A dog falling from a tall building
(no air resistance)
speed
Area = height of building
time
Acceleration/time graphs
acceleration
time
Constant/uniform acceleration?
acceleration
time
Note!
acceleration
The area under an
acceleration/time graph gives
the change in velocity
time
Displacement
• Displacement the distance moved in a
stated direction (the distance and direction
from the starting point). A VECTOR
Displacement/time graphs
• Usually in 1 dimension (+ = forward and - =
backwards)
Displacement/
m
Time/s
Velocity?
• Velocity is the rate of change of
displacement. Also a VECTOR
Velocity/time graphs
• Usually in 1 dimension (+ = forward and - =
backwards)
velocity/m.s-1
Ball being thrown into the air,
gradient = constant = -9.81 m.s-2
Time/s
Acceleration?
• Acceleration is the rate of change of
velocity. Also a VECTOR
Acceleration/time graphs
• Usually in 1 dimension (+ = up and - =
down)
accel/m.s-2
Acceleration = constant = -9.81
m.s-2
Time/s
Average speed/velocity?
• Average speed/velocity is change in
distance/displacement divided by time taken
over a period of time.
Instantaneous speed/velocity?
• Instantaneous speed/velocity is the change
in distance/displacement divided by time at
one particular time.
The equations of motion
• The equations of motion can be used when
an object is accelerating at a steady rate
• There are four equations relating five
quantities
u initial velocity, v final velocity,
s displacement, a acceleration, t time
SUVAT equations
NOT in
data book
1
The four equations
v = u + at
This is a re-arrangement of
a=
v-u
t
2
1
s = (v + u)t
2
This says displacement = average
velocity x time
3
1 2
s = ut + at
2
With zero acceleration, this
becomes displacement = velocity
x time
4
Useful when you don’t know the
v = u + 2as
time
2
2
Beware!
• All quantities are vectors (except time!).
These equations are normally done in one
dimension, so a negative result means
displacement/velocity/acceleration in the
opposite direction.
Example 1
Mr Blanchard is driving his car, when suddenly the
engine stops working! If he is travelling at 10 ms-1 and
his decceleration is 2 ms-2 how long will it take for the
car to come to rest?
Example 1
Mr Blanchard is driving his car, when suddenly the
engine stops working! If he is travelling at 10 ms-1 and
his decceleration is 2 ms-2 how long will it take for the
car to come to rest?
What does the question tell us. Write it out.
Example 1
Mr Blanchard is driving his car, when suddenly the
engine stops working! If he is travelling at 10 ms-1 and
his decceleration is 2 ms-2 how long will it take for the
car to come to rest?
u = 10 ms-1
v = 0 ms-1
a = -2 ms-2
t=?s
Example 1
Mr Blanchard is driving his car, when suddenly the
engine stops working! If he is travelling at 10 ms-1 and
his decceleration is 2 ms-2 how long will it take for the
car to come to rest?
u = 10 ms-1
v = 0 ms-1
a = -2 ms-2
t=?s
Choose the equation that has these quantities in
v = u + at
Example 1
Mr Blanchard is driving his car, when suddenly the
engine stops working! If he is travelling at 10 ms-1 and
his decceleration is 2 ms-2 how long will it take for the
car to come to rest?
u = 10 ms-1 v = 0 ms-1 a = -2 ms-2 t = ? s
v = u + at
0 = 10 + -2t
2t = 10
t = 5 seconds
Example 2
Jan steps into the road, 30 metres from where Mr
Blanchard’s engine stops working. Mr Blanchard does
not see Jan. Will the car stop in time to miss hitting
Jan?
Example 2
Jan steps into the road, 30 metres from where Mr
Blanchard’s engine stops working. Mr Blanchard does
not see Jan. Will the car stop in time to miss hitting
Jan?
What does the question tell us. Write it out.
Example 2
Jan steps into the road, 30 metres from where Mr
Blanchard’s engine stops working. Mr Blanchard does
not see Jan. Will the car stop in time to miss hitting
Jan?
u = 10 ms-1
v = 0 ms-1
a = -2 ms-2
t=5s
s=?m
Example 2
Jan steps into the road, 30 metres from where Mr
Blanchard’s engine stops working. Mr Blanchard does
not see Jan. Will the car stop in time to miss hitting
Jan?
u = 10 ms-1 v = 0 ms-1 a = -2 ms-2 t = 5 s s = ? m
Choose the equation that has these quantities in
v2 = u2 + 2as
Example 2
Jan steps into the road, 30 metres from where Mr
Blanchard’s engine stops working. Mr Blanchard does
not see Jan. Will the car stop in time to miss hitting
Jan?
u = 10 ms-1 v = 0 ms-1 a = -2 ms-2 t = 5 s s = ? m
v2 = u2 + 2as
02 = 102 + 2x-2s
0 = 100 -4s
4s = 100
s = 25m, the car does not hit Jan. 
Example 3
• A ball is thrown upwards with a velocity of
24 m.s-1.
Example 3
• A ball is thrown upwards with a velocity of
24 m.s-1.
• When is the velocity of the ball 12 m.s-1?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball 12 m.s-1?
u = 24 m.s-1
a = -9.8 m.s-2 v = 12 m.s-1
t=?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball 12 m.s-1?
u = 24 m.s-1
a = -9.8 m.s-2 v = 12 m.s-1
t=?
v = u + at
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball 12 m.s-1?
u = 24 m.s-1
a = -9.8 m.s-2 v = 12 m.s-1
v = u + at
12 = 24 + -9.8t
-12 = -9.8t
t = 12/9.8 = 1.2 seconds
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball -12 m.s-1?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball -12 m.s-1?
u = 24 m.s-1
a = -9.8 m.s-2 v = -12 m.s-1
t=?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball -12 m.s-1?
u = 24 m.s-1
a = -9.8 m.s-2 v = -12 m.s-1
v = u + at
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• When is the velocity of the ball -12 m.s-1?
u = 24 m.s-1
a = -9.8 m.s-2 v = -12 m.s-1
v = u + at
-12 = 24 + -9.8t
-36 = -9.8t
t = 36/9.8 = 3.7 seconds
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the displacement of the ball at those
times? (t = 1.2, 3.7)
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the displacement of the ball at those
times? (t = 1.2, 3.7)
t = 1.2, v = 12, a = -9.8, u = 24 s = ?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the displacement of the ball at those
times? (t = 1.2, 3.7)
t = 1.2, v = 12, a = -9.8, u = 24 s = ?
s = ut + ½at2 = 24x1.2 + ½x-9.8x1.22
s = 28.8 – 7.056 = 21.7 m
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the displacement of the ball at those
times? (t = 1.2, 3.7)
t = 3.7, v = 12, a = -9.8, u = 24 s = ?
s = ut + ½at2 = 24x3.7 + ½x-9.8x3.72
s = 88.8 – 67.081 = 21.7 m (the same?!)
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the velocity of the ball 1.50 s after
launch?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the velocity of the ball 1.50 s after
launch?
u = 24, t = 1.50, a = -9.8, v = ?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the velocity of the ball 1.50 s after
launch?
u = 24, t = 1.50, a = -9.8, v = ?
v = u + at
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the velocity of the ball 1.50 s after
launch?
u = 24, t = 1.50, a = -9.8, v = ?
v = u + at
v = 24 + -9.8x1.50 = 9.3 m.s-1
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the maximum height reached by the
ball?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the maximum height reached by the
ball?
u = 24, a = -9.8, v = 0, s = ?
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the maximum height reached by the
ball?
u = 24, a = -9.8, v = 0, s = ?
v2 = u2 + 2as
0 = 242 + 2x-9.8xs
0 = 242 -19.6s
Example 3
• A ball is thrown upwards with a velocity of 24
m.s-1.
• What is the maximum height reached by the
ball?
u = 24, a = -9.8, v = 0, s = ?
0 = 242 -19.6s
19.6s = 242
s = 242/19.6 = 12.3 m
Imagine a dog being thrown out of an
aeroplane.
Woof!
(help!)
Force of gravity means the dog accelerates
gravity
To start, the dog is falling slowly (it has not
had time to speed up).
There is really only one force acting on the
dog, the force of gravity.
The dog falls faster (accelerates) due to this
force.
Gravity is still bigger than air resistance
Air resistance
As the dog falls faster, another force
becomes bigger – air resistance.
gravity
The force of gravity on the dog of course
stays the same
The force of gravity is still bigger than the air
resistance, so the dog continues to
accelerate (get faster)
Gravity = air resistance
Terminal velocity
Air resistance
As the dog falls faster and air resistance
increases, eventually the air resistance
becomes as big as (equal to) the force of
gravity.
The dog stops getting faster (accelerating)
and falls at constant velocity.
gravity
This velocity is called the terminal velocity.
Falling without air resistance
This time there is only one force acting in the
ball - gravity
gravity
Falling without air resistance
The ball falls faster….
gravity
Falling without air resistance
The ball falls faster and faster…….
gravity
Falling without air resistance
The ball falls faster and faster and faster…….
It gets faster by 9.81 m/s every second (9.81
m/s2)
This number is called “g”, the acceleration due
to gravity.
gravity
Falling without air resistance?
distance
time
Falling without air resistance?
speed
Gradient = acceleration = 9.8 m.s-2
time
Velocity/time graphs
Taking upwards are the positive direction
velocity/m.s-1
Ball being thrown into the air,
gradient = constant = -9.81 m.s-2
Time/s
Falling with air resistance?
distance
time
Falling with air resistance?
Terminal velocity
velocity
time
Gravity
What is gravity?
Gravity
Gravity is a force between ALL objects!
Gravity
Gravity
The size of the force depends on the mass of
the objects. The bigger they are, the bigger
the force!
Small attractive force
Bigger attractive force
Gravity
The size of the force also depends on the
distance between the objects.
Gravity
We only really notice the gravitational
attraction to big objects!
Hola! ¿Como estas?
Gravity
The force of gravity on something is called
its weight. Because it is a force it is
measured in Newtons.
Weight
Gravity
On the earth, Mr Spence’s weight is around
800 N.
I love
physics!
800 N
Gravity
On the moon, his weight is around 130 N.
Why?
130 N
Gravity
In deep space, far away from any planets or
stars his weight is almost zero. (He is
weightless). Why?
Cool!
Mass
Mass is a measure of the amount of material
an object is made of and also its resistance
to motion (inertia). It is measured in
kilograms.
Mass
Mr Spence has a mass of around 77 kg. This
means he is made of 77 kg of blood, bones,
hair and (mostly brain)!
77kg
Mass
On the moon, Mr Spence hasn’t changed
(he’s still Mr spence!). That means he still
is made of 77 kg of blood, bones and hair
and (mostly) brain!
77kg
Gravity
In deep space, Mr Spence still hasn’t
changed (he’s still Mr Spence!). That means
he still is made of 77 kg of blood, bones,
hair and brain!
I feel sick!
77kg
Calculating weight
To calculate the weight of an object you
multiply the object’s mass by the gravitational
field strength wherever you are.
Weight (N) = mass (kg) x gravitational field strength (N/kg)
Newton’s 1st Law
An object continues in uniform motion in
a straight line or at rest unless a resultant
external force acts
Newton’s first law
Galileo imagined a marble rolling in a very
smooth (i.e. no friction) bowl.
Newton’s first law
If you let go of the ball, it always rolls up the
opposite side until it reaches its original height
(this actually comes from the conservation of
energy).
Newton’s first law
No matter how long the bowl, this always
happens.
constant velocity
Newton’s first law
Galileo imagined an infinitely long bowl where
the ball never reaches the other side!
Newton’s first law
The ball travels with constant velocity until its reaches
the other side (which it never does!).
Galileo realised that this was the natural state of objects
when no (resultant ) forces act.
constant velocity
Another example
Imagine a man cycling at constant
velocity.
Newton’s 1st law
He is providing a pushing force.
Constant velocity
Newton’s 1st law
There is an equal and opposite
friction force.
Pushing force
friction
Constant velocity
Newton’s second law
Newton’s second law concerns examples
where there is a resultant force.
Let’s go back to the man on his
bike.
Remember when the forces are balanced (no
resultant force) he travels at constant
velocity.
Pushing force
friction
Constant velocity
Newton’s 2nd law
Now lets imagine what happens if
he pedals faster.
Pushing force
friction
Newton’s 2nd law
His velocity changes (goes faster).
He accelerates!
Remember from last year that acceleration
is rate of change of velocity. In other words
acceleration = (change in velocity)/time
Pushing force
friction
acceleration
Newton’s 2nd law
Now imagine what happens if he stops pedalling.
friction
Newton’s 2nd law
So when there is a resultant force,
an object accelerates (changes
velocity)
Pushing force
friction
Newton’s
nd
2
law
There is a mathematical relationship between
the resultant force and acceleration.
Resultant force (N) = mass (kg) x acceleration (ms-2)
FR = ma
It’s physics, there’s
always a
mathematical
relationship!
An example
Resultant force = 100 – 60 = 40 N
FR = ma
40 = 100a
a = 0.4 m/s2
Mass of Mr Porter and bike = 100
kg
Pushing force (100
N)
Friction (60
N)
Newton’s
rd
3
law
If a body A exerts a force on body B, body B will exert an
equal but opposite force on body A.
Hand (body A) exerts
force on table (body B)
Table (body B) exerts
force on hand (body A)
Free-body diagrams
Shows the magnitude and direction of all
forces acting on a single body
The diagram shows
the body only and
the forces acting on
it.
Examples
• Mass hanging on a rope
T (tension in
rope)
W (weight)
Examples
• Inclined slope
If a body touches
another body there is a
force of reaction or
contact force. The
force is perpendicular
to the body exerting
the force
F
(friction)
R (normal reaction
force)
W (weight)
Examples
• String over a pulley
T (tension in
rope)
W
T (tension in
rope)
1
W
Momentum
• Momentum is a useful quantity to consider
when thinking about "unstoppability". It is
also useful when considering collisions and
explosions. It is defined as
Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1)
p = mv
Law of conservation of
momentum
• The law of conservation of linear
momentum says that
“in an isolated system, momentum remains
constant”.
We can use this to calculate what happens after a collision (and in fact during an
“explosion”).
Law of conservation of
momentum
• In a collision between two objects,
momentum is conserved (total momentum
stays the same). i.e.
Total momentum before the collision = Total momentum after
Momentum is not energy!
A harder example!
• A car of mass 1000 kg travelling at 5 m.s-1
hits a stationary truck of mass 2000 kg.
After the collision they stick together. What
is their joint velocity after the collision?
A harder example!
Before
2000kg
1000kg
5 m.s-1
Momentum before = 1000x5 + 2000x0 = 5000 kg.m.s-1
After
Combined mass = 3000 kg
V m.s-1
Momentum after = 3000v
A harder example
The law of conservation of momentum tells us that
momentum before equals momentum after, so
Momentum before = momentum after
5000 = 3000v
V = 5000/3000 = 1.67 m.s-1
Momentum is a vector
• Momentum is a vector, so if velocities are
in opposite directions we must take this into
account in our calculations
An even harder example!
Snoopy (mass 10kg) running at 4.5
m.s-1 jumps onto a skateboard of mass
4 kg travelling in the opposite direction
at 7 m.s-1. What is the velocity of
Snoopy and skateboard after Snoopy
has jumped on?
I love
physics
An even harder example!
Because they are in opposite directions,
we make one velocity negative
10kg
-4.5 m.s-1
7 m.s-1
4kg
Momentum before = 10 x -4.5 + 4 x 7 = -45 + 28 = -17
14kg
v m.s-1
Momentum after = 14v
An even harder example!
Momentum before = Momentum after
-17 = 14v
V = -17/14 = -1.21 m.s-1
The negative sign tells us that the
velocity is from left to right (we
choose this as our “negative
direction”)
“Explosions” - recoil
Impulse
Ft = mv – mu
The quantity Ft is called the impulse, and of course
mv – mu is the change in momentum (v = final
velocity and u = initial velocity)
Impulse = Change in momentum
Impulse
Ft = mv – mu
F = Δp/Δt
Units
Impulse is measured in N.s (Ft)
or kg.m.s-1 (mv – mu)
5 m/s
-3 m/s
Impulse
Note; For a ball bouncing off a wall, don’t forget
the initial and final velocity are in different
directions, so you will have to make one of them
negative.
In this case mv – mu = -3m -5m = -8m
Example
• Szymon punches Eerik in the face. If Eerik’s head (mass 10 kg)
was initially at rest and moves away from Szymon’s fist at 3 m/s,
what impulse was delivered to Eerik’s head? If the fist was in
contact with the face for 0.2 seconds, what was the force of the
punch?
• m = 10kg, t = 0.2, u = 0, v = 3
• Impulse = Ft = mv – mu = 10x3 – 10x0 = 30 Ns
• Impulse = Ft = 30
Fx0.2 = 30
F = 30/0.2 = 150 N
Another example
• A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the
opposite direction at 6 m/s. What impulse is given to the ball?
• Impulse = mv – mu =
= 0.3x-6 – 0.3x3
= -2.7kg.m.s-1
3 m/s
-6 m/s
Area under a force-time graph = impulse
Area = impulse
Work
In physics, work has a
special meaning,
different to “normal”
English.
Work
In physics, work
is the amount of
energy
transformed
(changed) when a
force moves (in
the direction of
the force)
Calculating work
The amount of work done (measured in
Joules) is equal to the force used (Newtons)
multiplied by the distance the force has
moved (metres).
Force (N)
Distance
travelled (m)
Work (J)= Force(N) x distance(m)
W = Fscosθ
Important
The force has to be
in the direction of
movement.
Carrying the
shopping home is
not work in physics!
What if the force is at an angle to the
distance moved?
Work = Fscosθ
F
θ
s
Lifting objects
Our lifting force is equal to the weight of
the object.
Lifting force
weight
Work done (J) = Force (N) x distance (m)
A woman pushes a car with a force of 400 N at
an angle of 10° to the horizontal for a distance
of 15m. How much work has she done?
W = Fscosθ = 400x15x0.985
W = 5900 J
Work done (J) = Force (N) x distance (m)
A man lifts a mass of 120 kg to a height of
2.5m. How much work did he do?
Force = weight = 1200N
Work = F x d = 1200 x 2.5
Work = 3000 J
Power!
Power is the amount of energy transformed
(changed) per second. It is measured in
Watts (1 Watt = 1 J/s)
Power = Energy transformed
time
Work done in stretching a spring
Work done in strectching spring = area under graph
F/N
x/m
Chemical
kinetic
gravitational
Gain in GPE = work done = m x g x Δh
ΔEp = mgΔh
m
Joules
kg
N/kg or m/s2
Kinetic energy
Kinetic energy of an object can be found
using the following formula
Ek = mv2
2
where m = mass (in kg) and v = speed (in m/s)
Example
A bullet of mass 150 g is travelling at 400 m/s.
How much kinetic energy does it have?
Ek = mv2/2 = (0.15 x (400)2)/2 = 12 000 J
Energy changes
Energy transfer (change)
A lamp turns
electrical
energy into heat
and light
energy
Sankey Diagram
A Sankey diagram helps to show how much
light and heat energy is produced
Sankey Diagram
The thickness of each arrow is drawn to
scale to show the amount of energy
Sankey Diagram
Notice that the total amount of energy
before is equal to the total amount of energy
after (conservation of energy)
Efficiency
Although the total energy out is the same,
not all of it is useful.
Efficiency
Efficiency is defined as
Efficiency
= useful energy output
total energy input
Example
Efficiency = 75 = 0.15
500
Energy efficient light bulb
Efficiency = 75 = 0.75
100
That’s much
better!
Elastic collisions
• No loss of kinetic energy (only collisions
between subatomic particles)
Inelastic collisions
• Kinetic energy lost (but momentum stays
the same!)
Satellites
Small cannon
Gravity
Bigger cannon
Gravity
Gravity
Even bigger cannon
Gravity
Gravity
Gravity
VERY big cannon
Gravity
Humungous cannon?
Other examples
Earth’s
gravitational
attraction on moon
Uniform Circular Motion
• This describes an object going around a
circle at constant speed
Direction of centripetal
acceleration/force
Change in velocity
VB
VA
VB
VA
VA + change in velocity = VB
The change in velocity (and thus the
acceleration) is directed towards the centre of
the circle.
Uniform circular motion
The centripetal acceleration/force is always directed towards
the centre of the circle
Centripetal force/acceleration
velocity
Not uniform velocity
• It is important to remember that though the
speed is constant, the direction is changing
all the time, so the velocity is changing.
Uniform speed ≠ uniform velocity
How big is the centripetal
acceleration?
a=
2=
2
v 4π r
r
2
T
where a is the centripetal acceleration (m.s-2), r is the
radius of the circle (m), and v is the constant speed
(m.s-1).
How big is the centripetal force?
F=
2
mv
r
from F = ma (Newton’s 2nd law)
Centripetal Force - The Real Force
Work done?
• None! Because the force is always
perpendicular to the motion, no work is
done by the centripetal force.
That’s it!